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Math Help - Sigma Notation Help

  1. #1
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    Exclamation Sigma Notation Help

    We've had a couple of classes on the topic with geometric sequences and arithmetic series as well. I've been having a propblem finding the values to use in the sum of the geometric sequence formula.
    <br />
tn=\frac{ar^n-1}{r-1}<br />
    8
    <br />
\sum(1/3)^(k-9)<br />
    k=4
    I`m having trouble getting the a and r values,is there any general rules you can use when looking for them in sigma notation
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  2. #2
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    Quote Originally Posted by nightrider456 View Post
    We've had a couple of classes on the topic with geometric sequences and arithmetic series as well. I've been having a propblem finding the values to use in the sum of the geometric sequence formula.
    <br />
tn=\frac{ar^n-1}{r-1}<br />
    8
    <br />
\sum(1/3)^(k-9)<br />
    k=4
    I`m having trouble getting the a and r values,is there any general rules you can use when looking for them in sigma notation
    I take it that this is actually

    \sum_{k = 4}^8 \left(\frac{1}{3}\right)^{k - 9}.


    Why not try writing out the first few terms?

    \sum_{k = 4}^8 \left(\frac{1}{3}\right)^{k - 9} = \left(\frac{1}{3}\right)^{-5} + \left(\frac{1}{3}\right)^{-4} + \left(\frac{1}{3}\right)^{-3} + \dots

     = 243 + \frac{1}{3}\cdot 243 + \frac{1}{3}\cdot \frac{1}{3} \cdot 243 + \dots.


    Can you see what a and r are now?
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